Skip to main content
Log in

A Review on Kalman Filter Models

  • Review Article
  • Published:
Archives of Computational Methods in Engineering Aims and scope Submit manuscript

Abstract

Kalman Filter (KF) that is also known as linear quadratic estimation filter estimates current states of a system through time as recursive using input measurements in mathematical process model. Thus algorithm is implemented in two steps: in the prediction step an estimation of current state of variables in uncertainty conditions is presented. In the next step, after obtaining the measurement, previous estimation is updated by weighted arithmetic mean. Accordingly, using KF in non-linear systems can be difficult. For nonlinear systems Extended KF (EKF) and Unscented KF (UKF) represent the first-order and higher order linear approximations. KF cannot predict appropriate values for modeling system behavior in more complicated systems. In the current study, in addition to referring to basic methods, a review on recent researches on Multiple Model (MM) filters has been done. More reliable estimations obtain by using two or more filters with different models in parallel, by allocating an estimation to each filter, outputs of each filter are calculated. MM Adaptive Estimation (MMAE) and Interacting MM (IMM) are the most used methods for estimating MMs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Kalman RE (1960) A new approach to linear filtering and prediction problems. J Basic Eng 82(1):35–45

    Article  MathSciNet  Google Scholar 

  2. Kelly A (1994) A 3D state space formulation of a navigation Kalman filter for autonomous vehicles. Carnegie-Mellon University Robotics Institute, Pittsburgh

    Book  Google Scholar 

  3. Reid I, Term H (2001) Estimation II. Lecture notes. University of Oxford, Oxford

  4. Bishop G, Welch G (2001) An introduction to the Kalman filter. In: Proceedings of SIGGRAPH, course, 2001, vol 8(27599-23175), p 41

  5. Deng Z (2003) Kalman filter and the Wiener filter: modern time series analysis method. Press of Harbin Institute of Technology, Harbin

    Google Scholar 

  6. Huang X, Wang Y (2015) The Kalman filter principle and application. Publishing House of Electronics Industry, Beijing

    Google Scholar 

  7. Wolpert DM, Ghahramani Z (2000) Computational principles of movement neuroscience. Nat Neurosci 3(11):1212–1217

    Article  Google Scholar 

  8. Kang-Hua T, Mei-Ping W, Xiao-Ping H (2007) Multiple model Kalman filtering for MEMS-IMU/GPS integrated navigation. In: 2007 2nd IEEE conference on industrial electronics and applications, 2007. IEEE

  9. Xie L, Soh YC, De Souza CE (1994) Robust Kalman filtering for uncertain discrete-time systems. IEEE Trans Autom Control 39(6):1310–1314

    Article  MathSciNet  MATH  Google Scholar 

  10. Julier SJ, Uhlmann JK (1997) New extension of the Kalman filter to nonlinear systems. In: Signal processing, sensor fusion, and target recognition VI, 1997. International Society for Optics and Photonics

  11. Gao B et al (2017) Interacting multiple model estimation-based adaptive robust unscented Kalman filter. Int J Control Autom Syst 15(5):2013–2025

    Article  Google Scholar 

  12. Gustafsson F, Hendeby G (2011) Some relations between extended and unscented Kalman filters. IEEE Trans Signal Process 60(2):545–555

    Article  MathSciNet  MATH  Google Scholar 

  13. Arasaratnam I, Haykin S (2009) Cubature Kalman filters. IEEE Trans Autom Control 54(6):1254–1269

    Article  MathSciNet  MATH  Google Scholar 

  14. Wan M, Li P, Li T (2010) Tracking maneuvering target with angle-only measurements using IMM algorithm based on CKF. In: 2010 International conference on communications and mobile computing, 2010. IEEE

  15. Duan J et al (2016) Square root cubature Kalman filter-Kalman filter algorithm for intelligent vehicle position estimate. Procedia Eng 137:267–276

    Article  Google Scholar 

  16. Farahi F, Yazdi HS (2020) Probabilistic Kalman filter for moving object tracking. Signal Process Image Commun 82:115751

    Article  Google Scholar 

  17. Forney GD (1973) The Viterbi algorithm. Proc IEEE 61(3):268–278

    Article  MathSciNet  Google Scholar 

  18. Forney GD Jr (2005) The Viterbi algorithm: a personal history. arXiv preprint cs/0504020

  19. Xiong K, Wei C, Liu L (2015) Robust multiple model adaptive estimation for spacecraft autonomous navigation. Aerosp Sci Technol 42:249–258

    Article  Google Scholar 

  20. Hanlon PD, Maybeck PS (2000) Multiple-model adaptive estimation using a residual correlation Kalman filter bank. IEEE Trans Aerosp Electron Syst 36(2):393–406

    Article  Google Scholar 

  21. Seah CE, Hwang I (2009) State estimation for stochastic linear hybrid systems with continuous-state-dependent transitions: an IMM approach. IEEE Trans Aerosp Electron Syst 45(1):376–392

    Article  Google Scholar 

  22. Li XR, Jilkov VP (2005) Survey of maneuvering target tracking. Part V. Multiple-model methods. IEEE Trans Aerosp Electron Syst 41(4):1255–1321

    Article  Google Scholar 

  23. Izadian A, Famouri P (2010) Fault diagnosis of MEMS lateral comb resonators using multiple-model adaptive estimators. IEEE Trans Control Syst Technol 18(5):1233–1240

    Article  Google Scholar 

  24. Yang R et al (2011) RF emitter geolocation using amplitude comparison with auto-calibrated relative antenna gains. IEEE Trans Aerosp Electron Syst 47(3):2098–2110

    Article  Google Scholar 

  25. Magill D (1965) Optimal adaptive estimation of sampled stochastic processes. IEEE Trans Autom Control 10(4):434–439

    Article  MathSciNet  Google Scholar 

  26. Blom HA, Bar-Shalom Y (1988) The interacting multiple model algorithm for systems with Markovian switching coefficients. IEEE Trans Autom Control 33(8):780–783

    Article  MATH  Google Scholar 

  27. Li X-R, Bar-Shalom Y (1996) Multiple-model estimation with variable structure. IEEE Trans Autom Control 41(4):478–493

    Article  MathSciNet  MATH  Google Scholar 

  28. Chang C-B, Athans M (1977) Hypothesis testing and state estimation for discrete systems with finite-valued switching parameters. Massachusetts Institute of Technology Cambridge Electronic Systems Lab

  29. Chang C-B, Athans M (1978) State estimation for discrete systems with switching parameters. IEEE Trans Aerosp Electron Syst 3:418–425

    Article  MathSciNet  Google Scholar 

  30. Hawkes RM, Moore JB (1976) Performance bounds for adaptive estimation. Proc IEEE 64(8):1143–1150

    Article  MathSciNet  Google Scholar 

  31. Lainiotis DG (1976) Partitioning: A unifying framework for adaptive systems, I: Estimation. Proc IEEE 64(8):1126–1143

    Article  MathSciNet  Google Scholar 

  32. Lashlee RW, Maybeck PS (1988) Space structure control using moving bank multiple model adaptive estimation. In: Proceedings of the 27th IEEE conference on decision and control, 1988. IEEE

  33. Morales-Menéndez R (n.d.) Real-time monitoring and diagnosis in dynamic systems using particle filtering methods. Edición Única

  34. Kay SM (1988) Modern spectral estimation: theory and application. Pearson Education India, Englewood Cliffs

    MATH  Google Scholar 

  35. Xiong K, Wei C, Liu L (2012) Robust Kalman filtering for discrete-time nonlinear systems with parameter uncertainties. Aerosp Sci Technol 18(1):15–24

    Article  Google Scholar 

  36. Kottath R et al (2015) Improving multiple model adaptive estimation by filter stripping. In: 2015 IEEE recent advances in intelligent computational systems (RAICS), 2015. IEEE

  37. Hide C, Moore T, Smith M (2004) Adaptive Kalman filtering algorithms for integrating GPS and low cost INS. In: PLANS 2004. Position location and navigation symposium. IEEE Cat. No. 04CH37556, 2004. IEEE

  38. Mohamed A, Schwarz K (1999) Adaptive Kalman filtering for INS/GPS. J Geod 73(4):193–203

    Article  MATH  Google Scholar 

  39. Kottath R et al (2016) Window based multiple model adaptive estimation for navigational framework. Aerosp Sci Technol 50:88–95

    Article  Google Scholar 

  40. Hwang I, Balakrishnan H, Tomlin C (2003) Performance analysis of hybrid estimation algorithms. In: 42nd IEEE international conference on decision and control (IEEE Cat. No. 03CH37475), 2003. IEEE

  41. Akca A, Efe MÖ (2019) Multiple model Kalman and Particle filters and applications: a survey. IFAC-PapersOnLine 52(3):73–78

    Article  Google Scholar 

  42. Orguner U (2013) EE793 target tracking. Lecture notes

  43. Gao L et al (2012) Improved IMM algorithm for nonlinear maneuvering target tracking. Procedia Eng 29:4117–4123

    Article  Google Scholar 

  44. Sun L, Shen C (2014) An improved interacting multiple model algorithm used in aircraft tracking. Math Probl Eng 20:14. https://doi.org/10.1155/2014/813654

    Article  Google Scholar 

  45. Hu G et al (2015) Modified strong tracking unscented Kalman filter for nonlinear state estimation with process model uncertainty. Int J Adapt Control Signal Process 29(12):1561–1577

    Article  MathSciNet  MATH  Google Scholar 

  46. Jwo D-J, Weng T-P (2008) An adaptive sensor fusion method with applications in integrated navigation. IFAC Proc Vol 41(2):9002–9007

    Article  Google Scholar 

  47. Song H, Hu S (2019) Open problems in applications of the Kalman filtering algorithm. In: 2019 International conference on mathematics, big data analysis and simulation and modelling (MBDASM 2019), 2019. Atlantis Press

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vafa Maihami.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khodarahmi, M., Maihami, V. A Review on Kalman Filter Models. Arch Computat Methods Eng 30, 727–747 (2023). https://doi.org/10.1007/s11831-022-09815-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11831-022-09815-7

Navigation